Answer
The probability of getting a tail in all the seven tosses is $\frac{1}{128}$.
Work Step by Step
We know that the probability of getting a tail in a single toss of the coin is as follows:
Number of favorable out comes $ n\left( e \right)=1$ (tail)
Number of total out comes $ n\left( s \right)=2$ (head and tail)
$ P\left( \text{tails} \right)=\frac{1}{2}$
And the probability of getting a tail in all the seven tosses is given below,
$\begin{align}
& P\left( \text{seven tails} \right)=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} \\
& =\frac{1}{128}
\end{align}$
Thus, the probability that a tail will come in all the seven tosses is $\frac{1}{128}$.
